Discrete Mathematics Revision Quiz

Study Notes

Algebraic Identities:
- a² = 2ab + b² = (ab)²
- x² - a² = (x + a)(x - a)
Trigonometric Identities:
- sin x
- csc(-x) = -csc(x)
- cot(-x) = -cot(x)
- sech(x) = (e⁻ˣ + eˣ)/2
- coth²(z) = csch²(z) - 1
- various trigonometric formulas involving sin, cos, tan, cot, sec, csc, sinh, cosh, tanh, coth, sech, csch
Other Formulas:
- xₙ₊₁ = (xₙ/2)(3 - a xₙ²)
- Various formulas related to series and sequences (Sn, aₙ, etc.)
- ~Vx[~p(x)] =∃x[p(x)]
- ~(p∧q) = ~p∨~q
- Various formulas related to sets, logic, and discrete math

Logical Connectives:
- And (Conjunction): ∧ (p∧q)
- Or (Disjunction): ∨ (pvq)
- If...then (Implication): → (p→q)
- If and only if (Biconditional): ↔ (p↔q)
- Not (Negation): ~ (~p)
Truth Tables: Truth tables for all the logical connectives are presented, showing the output based on input combination
Types of Statements:
- Tautology (always true)
- Contradiction (always false)
- Contingency (neither always true nor always false)
Converse, Contrapositive, Inverse:
- Converse (q→p)
- Contrapositive (~q→~p)
- Inverse (~p→~q)
Negation of Statements:
- ~(p∨q) = ~p∧~q
- ~(p∧q) = ~p∨~q
- ~(p→q) = p∧~q
Logical Equivalence and Duality:
- Duals/Equivalent statements involving the substitution of ∧ and ∨ (and vice-versa)
Mathematical Logic Application to Switching Circuits:
- AND, OR, truth tables, and their relation to switches and circuits explained
Sets and Logic Various formulas and explanations about sets, and logic presented in the document, including different types of propositions, compound statements, and logical connective notation.

Problem types: Includes a variety of problem-solving examples related to statements, logical connectives, and their applications. (Page 4 onward)
Identify unknown: Involves working through symbolic representations and identifying the specific meaning of the problems (Page 4 onward)
Conversions: Examples converting verbal statements into their symbolic counterparts (Page 4 onward)